A senior Iranian official with close links to the country's president and supreme leader has offered his congratulations to Iraq's prime minister-designate, suggesting Tehran has abandoned former ally Nouri al-Maliki amid the current Sunni militant insurgency.

Ali Shamkhani, the secretary of Iran's powerful Supreme National Security Council, was quoted by the official IRNA news agency congratulating the Iraqi people and their leaders for choosing Haider al-Abadi as their new prime minister.

Abadi, a veteran of Iraq's post-Saddam Hussein governments, was appointed on Monday after the country's president effectively deposed Maliki in an effort to break the political deadlock that has paralysed the government while jihadists sweep through the north of the country.

Shamkhani, a close ally of President Hassan Rouhani and a representative of Ayatollah Ali Khamenei on the council, said Iran supported "the legal process for choosing the new Iraqi prime minister".

The US secretary of state, John Kerry, said earlier on Tuesday that Washington was ready to "fully support a new and inclusive Iraqi government". While attending the annual Ausmin talks in Australia, Kerry urged Abadi to form a functional cabinet "as swiftly as possible" and said the US was ready to offer more military and economic help.

"We are prepared to consider additional political, economic and security options as Iraq's government starts to build a new government," he said in Sydney.

Hossein Rassam, a London-based Iranian analyst, said Shamkhani's statement reflect Tehran's hand in al-Abadi's appointment: "His appointment could not have materialised without Iran's cooperation. This is the result of a series of negotiations and bargaining for the past number of days, it's not something that has been decided overnight."

According to Rassam, Iran's top priority in Iraq has been to avoid a power vacuum in Baghdad and ensure the appointment of a prime minister sympathetic to Tehran. "With Abadi's appointment, Iran has achieved both," he said.

Ali Alizadeh, an Iranian political analyst, said Iran's welcome of the new government, and tacit support of the western governments, was "a correct pragmatic compromise".

"It shows Iran's priority is to contain Isis rather than wasting time to haggle over the amount of its influence on the Iraqi government," Alizadeh said.

Hayder al-Khoei, an Iraq expert at the London-based Chatham House thinktank, said it also signalled the death of Maliki's political life, but that he could still cause problems for the incoming government.

"We can't predict how he is going to react," he told the BBC. "He can still cause a lot of problems for the political process and his rivals. He is framing this as an illegal, unconstitutional attempt to unseat him. And he is being pushed into a corner."

Khoei said that even if Abadi succeeded in forming a unity government, Iraq still faced a grim and fragmented future.

"Iraq as a nation state, as we have known it, is not going to return. The best-case scenario is a much more decentralised country. The worst-case scenario will be de facto partition, more civil war, more bloodshed and ethnic cleansing on a much wider scale."

Kerry made it clear that US offers of military assistance to an Abadi government did not mean a return of US troops.

"There will be no reintroduction of American combat forces into Iraq," he said. "Nobody, I think, is looking forwards to a return to the road that we've travelled.

"What we're really looking for here is a way to support Iraq, support their forces with either training or equipment or assistance of one kind or another, that can help them to stand on their own two feet and defend their nation."

The international community has repeatedly put pressure on Maliki to step down since the start of the jihadist insurrection in June that saw Mosul, Tikrit and much of western Iraq fall to Isis, and Kirkuk fall to the Kurds.

The Iraqi army abandoned its posts in the north in one of the more spectacular routs in modern military history. The retreating forces left behind US-made military equipment which Isis used to launch another assault this month.

A week of devastating gains resulted in the jihadists taking the country's largest dam while attacks on Christian, Yazidi, Turkmen and Shabak minorities around Mosul saw the number of Iraqis displaced this year rise to more than 1 million.

US air strikes, which began last week, have reinvigorated Iraqi Kurdish forces battling the Islamic State. On Sunday, the Kurdish peshmerga fighters retook two towns from the Sunni militants in what was one of their first victories after weeks of retreat. But in the eastern Diyala province, Kurdish forces were driven out on Monday from the town of Jalula after fierce fighting with the militants.

US and British military jets have begun air drops of humanitarian aid to displaced Iraqis, including Yazidi refugees besieged by Isis on Mount Sinjar in northern Iraq.